This invention relates to an arrangement for the fluorescence-optical measurement of the concentration of substances contained in a sample, comprising a light source for excitation radiation, a sensor element fluorescing upon excitation in accordance with the substance concentration to be determined, and a detector for emission radiation, the sensor element comprising a carrier element which can be brought into contact, at least indirectly, with the sample to be measured via at least part of its surface, and which is transparent for excitation and emission radiation and has a refractive index n.sub.1 that is higher than the refractive index n.sub.3 of the ambient medium so that light rays, whose angles of incidence .alpha..sub.1 --measured from the normal on the boundary surface between carrier element and ambient medium--are bigger than .alpha..sub.G.sbsb.1.3 =arc sin n.sub.3 /n.sub.1, arc propagated in the carrier element by total reflection.